On fuzzy multiattribute decision-making models and methods with incomplete preference information

In the paper by Li (Fuzzy Sets and Systems 106 (1999) 113), a minimum average weighted deviation method was investigated to determine the weights of attributes using incomplete preference information. It is shown in this paper that the method is flawed and can only be meaningful if it is revised. Two general ways are presented to revise it and are justified by using Lagrange multiplier method and Hessian matrix. Four specific revised models and approaches are investigated and examined through a numerical example. Different membership functions are suggested and utilized to normalize decision matrix so that a credible ranking order can be achieved.